BANK & INSURANCE (AVERAGE) PART 2

Total Questions: 45

31. There are 18 students in a class. Average weight of the class increased by 1 kg, when two new students A and B joined in the class. If A only joined the class, the average weight of the class is increased by 2 kg and ratio of the weight of A to B is 11 : 4, then find the average weight of the class initially?

Correct Answer: (b) 50 kg  
Solution:Total weight of the class initially = 18x
Average weight after added A and B = x + 1
Average weight of the class after added A = x + 2
18x + A + B = 20 × (x + 1): 18x + A + B = 20x + 20
A + B = 2x + 20
18x + A = 19 × (x + 2): 18x + A = 19x + 38
x + 38 = A
x + 38 + B = 2x + 20
x - 18 = B
A/B = 11/4
4A = 11B
4(x + 38) = 11(x - 18): 4x + 152 = 11x - 198
7x = 350
x = 50 kg

32. Four years ago, the average age of the class is 24 years. Two years ago one student left the class with age of 29 years and after one year the new student joined the class with the age of 24 years. If the initial number of students in the class is 16, then find the present approximate average age of the class?

Correct Answer: (a) 27.6 years  
Solution:

Four years ago the total age of the class
= 24 × 16 = 384
Two years ago the total age of the class
= 384 + 16 × 2 - 29 = 387

One year ago the total age of the class
= 387 + 24 + 15 = 426
Present age of all the students = 426 + 16 = 442
Average age = 442 / 16 = 27.625 years

33. The weight of A is 12 kg less than the weight of B and weight of B is 18 kg more than the weight of C. The average weight of A, B, C is 26 kg. If the ratio of the weight of B to that of D is 2:3, then find the weight of D.

Correct Answer: (c) 54 kg
Solution:A + B + C = 78 kg
A = B - 12
B = C + 18
A = C + 18 - 12 = C + 6
C + 6 + (C + 18 + C = 78
3C = 54
C = 18 kg
B = 18 + 18 = 36 kg
D = 3/2 × 36 = 54 kg

34. The Average marks obtained by 45 students in an examination are 12. If the average marks of passed students are 14 and that of failed students are 5, then find the number of students who are passed in the examination?

Correct Answer: (a) 35  
Solution:

Let the number of passed students be x,
45 × 12 = 14x + (45 - x) × 5
540 = 14x + 225 - 5x
540 - 225 = 9x
9x = 315
x = 35
Total number of passed students = 35

Shortcut:

14     5
...........12
-7    -2

⇒ 7 : 2
9’s = 45
1’s = 5
Total number of passed students = 7’s = 35

35. The average weight of 50 students in a class was calculated as 35 kg. It was later found that the weight of three students in the class was wrongly calculated. The actual weight of one of the boys in the class was 34kg, but it was calculated as 38 kg and the actual weight of second boy in the class was 42 kg whereas it was calculated as 45 kg and the weight of third boy in the class was 38 kg, whereas it was calculated as 41 kg. What is the actual average weight of the 50 students in the class?

Correct Answer: (b) 34.8 kg  
Solution:Sum of actual weight of three boys = 34 + 42 + 38 = 114 kg
Sum of wrongly calculated weight of three boys
= 38 + 45 + 41 = 124 kg
Difference = 124 - 114 = 10 kg
Actual average of 50 students
= 35 - 10/50 = 35 - 0.2 = 34.8 kg

36. The average of four values a, b, c and d is 35. The average of a and c is 5 more than the average of b and d. The average of a and c is greater than b by 3. Find the value b.

Correct Answer: (c) 34.5
Solution:

ATQ,
(a+b+c+d)/4 = 35
(a+b+c+d) = 140 ..............(1)

(a+c)/2 - (b+d)/2 = 5
(a+c) - (b+d) = 10 ..............(2)

Adding equation, (1) and (2), we get
2(a+c) = 150
a + c = 75

Again, ATQ
(a+c)/2 - b = 3
75/2 - b = 3
b = 75/2 - 3
b = 37.5 - 3
b = 34.5

37. A quiz is attended by two students A and B. For each correct answer, 2 marks is awarded, for each wrong answer 25% of the mark will be deducted from the marks obtained from the correct answer, no mark will be deducted for not attending a question. The average mark of the two students is 80. The average number of correct questions is 45. Find the average number of questions not attended by both, if the total number of questions is 90.

Correct Answer: (e) 25
Solution:

Number of questions = 90
Average of marks = 80
Total marks of A and B = 2 × 80 = 160
Average number of correct questions = 45
Total number of correct questions = 2 × 45 = 90
Let W be the total number of wrong questions
% wrong questions = -25% of 2 = -0.5
90 × 2 - 0.5 W = 160

0.5W = 180 - 160 = 20
W = 40
Number of questions not attended
= 180 - 90 - 40 = 50
Average number of questions not attended
= 50/2 = 25

38. In a company, 60% of the workers are apprentice. All the remaining workers are company employees. The monthly income of each apprentice is Rs.4000. The monthly income of each company employee is Rs.8000. What is the average monthly income of all the workers in the company?

Correct Answer: (d) Rs.5600  
Solution:Let e be the number of workers.
60% of the workers are apprentice, 60/100×e = 0.6e
Number of company employees
= (The number of workers) - (The number of apprentice) = e - 0.6e = 0.4e
The monthly income of each apprentice is Rs.4000
The monthly income of each employee is Rs.8000
Hence, the total income of the workers = (0.6e × 4000) + (0.4e × 8000) = 2400e + 3200e = 5600e
Required average = Total income/Number of workers = 5600e/e = Rs.5600

39. The average of nine numbers is 30, out of which average of 8th number and 9th number is 33/2 and the average of the 4th, 5th, 6th and 7th numbers is 147/4. The 3rd number is less than the 2nd number and the 1st number by 6 and 9 respectively. Find the 2nd number.

Correct Answer: (b) 31  
Solution:Sum of nine numbers = 30 × 9 = 270
Sum of 8th and 9th numbers = 33/2 × 2 = 33
Sum of 4th, 5th, 6th and 7th numbers = 147/4 × 4 = 147
Sum of last six numbers = 33 + 147 = 180
So, sum of 1st, 2nd and 3rd numbers = 270 - 180 = 90
Let the 3rd number be x
Then, 2nd number = x + 6 and 1st number = x + 9
Now,
⇒ x + x + 6 + x + 9 = 90
⇒ 3x + 15 = 90
⇒ 3x = 75
⇒ x = 25
Hence, 2nd number = 25 + 6 = 31

40. A class have 20 students. If in the quarterly exam, the average marks of first 8 students is 200 less than the average marks scored by last 12 students in the half yearly exam, the average marks scored by last 12 students is decreased by 120 compared to Quarterly exam’s average but the average marks scored by all the students in the class is increased by 80 compared to Quarterly exam’s average. Find the increased average marks scored by first 8 students?

Correct Answer: (d) 380  
Solution:

Quarterly exam:
Let Average mark scored by first 8 students = x
Total mark scored by first 8 students = 8x
Let Average mark scored by last 12 students = y
Total mark scored by last 12 students = 12y
Average marks by class = (8x + 12y)/20
y - x = 200

Half yearly exam:
Average marks scored by last 12 students = y - 120
Average marks scored by all the students = (8x + 12y)/20 + 80 = (8x + 12y + 1600)/20
Total marks scored by first 8 students = (8x + 12y + 1600) - 12(y - 120) = 8x + 3040
Average scored by first 8 students = (8x + 3040)/8 = x + 380
Increased by = x + 380 - x = 380